A printing press of this type is known from DE-GM 9,208,023. Cylinders cantilevered at one end form spring-mass systems which tend to vibrate. For this reason, it is known from DE-GM 9,208,449, for a printing press of the aforementioned type, to damp the vibration of the cylinders mounted at one end by placing a ring on the free end region of the impression cylinder, the diameter of which ring corresponds to the diameter of the external cylinder described by the block. Placement of this ring on one end of the impression cylinder ensures that the former is supported by the counterpressure cylinder and screen roller or, in other words, rolls between the two, such that the free end of the impression cylinder is also damped between the impression cylinder and the screen roller. Although this known arrangement has already led to a considerable damping and suppression of the vibration of cantilevered cylinders, the printing executed by the end region of the impression cylinder is not optimal in all cases.